Defective items probability question.?

Question

Hi I'm working with probability as part of an engineering course, and I'm struggling with the following tutorial question: Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components, 35% contain one defective component while 15% contain two defective components. If two components are randomly selected from the batch. What are the probabilities associated with 0, 1 and 2 defective components being in the batch under each of the following conditions? a) Neither selected component is defective. b) One of the two components is defective. c) Both components are defective. I've considered using hypergeometric probability distribution for events P(35%) and P(15%) while comparing to P(50%) but this yields no result.

Answer 1

a) 50% * 100% <--- 100% of getting neither defective from the 50% batch

+ 35% * 9/10*8/9 <--- probability of getting no defectives from the 35% batch containing 1 defective

+ 15% * 8/10*7/9 <--- probability of getting no defectives from the 15% batch containing 2 defectives

b) 50% * 0%

+ 35% * 2/10 + 15% * 2/10 * 8/9

c) 50% * 0% + 35% * 0% + 15% * 2/10*1/9